Permanent magnet synchronous motors (PMSMs) are utilized in various applications because they have generally favorable efficiency characteristics relative to other types of motors. Typically, PMSMs have three separate electrical windings within the stator which are each powered by alternating current (AC) voltages Va, Vb, and Vc. In operation, the winding currents Ia, Ib, and Ic each oscillate at a frequency proportional to the rotor speed and are separated by 120 degrees in phase from one another. These winding currents induce a rotating magnetic field which may be out of phase with the rotor. The resulting shaft torque depends upon both the magnitude of the magnetic field and the phase angle relative to the rotor.
For convenience, the winding voltages and currents may be represented by vectors with respect to a rotating reference frame that rotates with the rotor. The mapping between rotor position and the rotating reference frame depends upon the number of poles in the motor. The voltage vector has a direct component Vd and a quadrature component Vq. Similarly, the current has a direct component Id and a quadrature component Iq. Vd, Vq, Id, and Iq do not oscillate based on rotor position.
In certain applications, such as electric vehicles and hybrid electric vehicles, electrical power is available from a non-oscillating direct current (DC) voltage source such as a battery. Therefore, inverters are utilized to convert the non-oscillating voltage Vdc into three oscillating voltages. Inverters contain a discrete number of switching devices and are therefore capable of supplying only a discrete number of voltage levels at each of the three motor terminals. For a 2-level inverter, at any moment in time, the switching devices are set to electrically connect each of the three AC motor terminals to either the positive or the negative DC terminal. Thus, eight switching states are available. Two of these switching states, in which all three AC terminals are connected to the same DC terminal, are called zero states. In the remaining six states, one AC terminal is connected to one of the DC terminals and the other two AC terminals are connected to the opposite DC terminal. The inverter is capable of switching rapidly among these eight states.
Some general characteristics of typical inverter-fed PMSMs are illustrated in FIG. 1. In this Figure, the horizontal axis represents rotor speed and the vertical axis represents rotor torque. The operating region depends upon the DC voltage Vdc. The positive speed, positive torque operating region at a reference DC voltage may be bounded as illustrated by solid lines 110, 112, and 114. At low speeds, the maximum available torque may be limited by a maximum winding current as indicated by line 110. Line 112 indicates a maximum available torque at higher speeds which is limited by the voltage. At point 116, called the corner point, both current and voltage are at their respective maximums. Dotted line 118 indicates the corresponding limit at a higher DC voltage above the reference DC voltage. Line 114 indicates an overall maximum rated speed.
PMSMs may generate either positive or negative torque and may rotate in either positive or negative directions. In the positive speed, negative torque quadrant, a PMSM acts as a generator converting mechanical energy into electrical energy. In this quadrant, the characteristics are similar to that shown in FIG. 1, although the minimum torque curve corresponding to the voltage limit may not be a mirror image of line 112. The negative speed region closely tracks the positive speed region rotated 180 degrees about the origin.
FIG. 2 illustrates typical characteristics of an inverter-fed PMSM with respect to the winding current in the rotor reference frame. In this Figure, the direct component Id is represented by the horizontal axis and the quadrature component Iq is represented by the vertical axis. Curve 210 represents different combinations of Id and Iq that would produce a particular output torque. Curves 212, 214, and 216 represent the combinations for progressively higher output torques. Although every point along each of these curves produces the same output torque, some combinations will be associated with higher losses than others. Line 218 represents the most efficient operating point for each level of torque. However, it is not always possible to operate at this condition. Point 220 represents the current that would be induced in the windings by the permanent magnets in the rotor as the rotor spins at a particular speed. The voltage applied by the inverter alters the winding current from this condition. Curve 222 represents the boundary of the conditions that are achievable by the inverter at a particular rotor speed and bus voltage level. At higher bus voltages or lower rotor speeds, the boundary expands as shown by dashed curve 224.